In my novel in verse, my character is found out on the highway when she gets into an accident. She ran away from her sister and the doctor, and they reported her missing, saying she was dangerous to herself and others. What would happen if you were found like that? Where would you go until family picked you up?
She was reported to the police, and they have reason to believe the reports are accurate? And the police are at the accident? I'd imagine they'd try to detain the character until they can sort out whether she really is dangerous. But assuming your character is an adult, she wouldn't have to go back to her family even if she was dangerous; private citizens can't hold people against their wills. And if your character is a juvenile and says the home environment is a problem, s/he wouldn't be returned without further investigation.
She was reported to the police because she was doing intense harm to herself, so she ran away. She's mentally unstable. And the police are at the crash. She's 35.
If you assume the crash was unrelated to her being reported then it's just the police responding to an accident. There's no guarantee those officers will know anything about the report from her family. In which case she can do whatever she wants after the accident, assuming she's not badly injured. However, if YOU want the police officers to know about her being reported then she's either going to a hospital for injuries from the accident or they can take her to a psychiatric hospital for evaluation. Keep in mind, I'm assuming today's society & American rules. Also, if family call the police and tell them you're dangerous to yourself that in itself isn't enough to prompt them to do anything. Dangerous to OTHERS can get a response. If she's someplace where they can go visit her they will, if she's off wandering the world they may put out a missing person's report on her but that won't mean they will go hunt for her. There's also the issue of who's saying this about her. I can't call the police and say my sister is acting crazy and expect them to come lock her up. There needs to be some clear cut evidence that she needs psychiatric help.